At home greet fantastic number (7)
I believe the answer is:
integer
'number' is the definition.
(integer is a kind of number)
'at home greet fantastic' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'fantastic' is an anagram indicator (a fantastic or improbable ordering of the letters).
'greet' anagrammed gives 'teger'.
'in'+'teger'='INTEGER'
(Other definitions for integer that I've seen before include "Gin tree (anag)" , "Say one" , "A whole number, not a fraction" , "Treeing (anag.)" , "The whole thing" .)